CS 301 Homework 1- Let Σ = {a, b}. Show that the language [2 marks] L...

CS 301 Homework

1- Let Σ = {a, b}. Show that the language [2 marks]

L =

is not regular.

Expert Solution

venereology answered 1 year ago

Let L ⊆ Σ ∗ and define S(L), the suffix-language of L, as S(L) = {w...

Let L ⊆ Σ ∗ and define S(L), the suffix-language of L, as S(L) = {w ∈ Σ ∗ | x = yw for some x ∈ L, y ∈ Σ ∗ } Show that if L is regular, then S(L) is also regular.

let sigma = {a,b,c}. Use the Pumping Lemma to show that the language L defined below...

let sigma = {a,b,c}. Use the Pumping Lemma to show that the language L defined below is not regular. L={ a^p c(bb)^q : q > p >1}

Let INFINITE PDA = {<M>|M is a PDA and L(M) is an infinite language}. Show that...

Let INFINITE PDA = {<M>|M is a PDA and L(M) is an infinite language}. Show that INFINITE PDA is decidable.

5. (a) Let σ = (1 2 3 4 5 6) in S6. Show that G...

5. (a) Let σ = (1 2 3 4 5 6) in S6. Show that G = {ε, σ, σ^2, σ^3, σ^4, σ^5} is a group using the operation of S6. Is G abelian? How many elements τ of G satisfy τ^2 = ε? τ^3 = ε? ε is the identity permutation. (b) Show that (1 2) is not a product of 3-cycles. Must be written as a proof! (c) If a^4 = 1 and ab = b(a^2) in a...

Let Σ ⊆ P rop(A). Show that Σ|− p iff Σ ∪ {¬p} is unsatisfifiable.

(The “conjugation rewrite lemma”.) Let σ and τ be permutations. (a) Show that if σ maps...

(The “conjugation rewrite lemma”.) Let σ and τ be permutations. (a) Show that if σ maps x to y then στ maps τ(x) to τ(y). (b) Suppose that σ is a product of disjoint cycles. Show that στ has the same cycle structure as σ; indeed, wherever (... x y ...) occurs in σ, (... τ(x) τ(y) ...) occurs in στ.

1. Let a < b. (a) Show that R[a, b] is uncountable

L= {x^a y^b z^c | c=a+b(mod 2)} .Create a DFA and NFA for the language L....

L= {x^a y^b z^c | c=a+b(mod 2)} .Create a DFA and NFA for the language L. Solution and explanation please..

Let X ∼ Normal(0, σ^2 ). (a) Find the distribution of X^2/σ^2 . (Hint: It is...

Let X ∼ Normal(0, σ^2 ). (a) Find the distribution of X^2/σ^2 . (Hint: It is a pivot quantity.) (b) Give an interval (L, U), where U and L are based on X, such that P(L < σ^2 < U) = 0.95. (c) Give an upper bound U based on X such that P(σ^2 < U) = 0.95. (d) Give a lower bound L based on X such that P(L < σ^2 ) = 0.95

Let a < c < b, and let f be defined on [a,b]. Show that f...

Let a < c < b, and let f be defined on [a,b]. Show that f ∈ R[a,b] if and only if f ∈ R[a, c] and f ∈ R[c, b]. Moreover, Integral a,b f = integral a,c f + integral c,b f .

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